In this paper we consider a diffeomorphism f of a compact manifold M which contracts an invariant foliation W with smooth leaves. If the differential of f on TW has narrow band spectrum, there exist coordinates Hx: Wx→ TxW in which f| W has polynomial form. We present a modified approach that allows us to construct maps Hx that depend smoothly on x along the leaves of W. Moreover, we show that on each leaf they give a coherent atlas with transition maps in a finite dimensional Lie group. Our results apply, in particular, to C1-small perturbations of algebraic systems.
All Science Journal Classification (ASJC) codes
- Geometry and Topology